Several large-scale sea ice simulations are performed over the last three decades using a coupled ocean-sea ice model under the same experimental setup but partly modifying the representation of snow physics in the model. The inter-simulation spread analysis yields that the simulated multi-year ice is sensitive to such changes while the seasonal sea ice, is rather dominantly driven by the external oceanic and atmospheric forcings. In the context of a thinning Arctic sea ice cover, those findings suggest that including snow processes in large-scale sea ice models is beneficial, if not necessary, to predict the timing of the Arctic multi-year ice disappearance, whereas the operational forecasting of first-year ice extent using fully coupled models will likely require improvement to the oceanic and atmospheric components themselves.